For each linear transformation below, state a basis for Ker(T), the Nullity of the transformation, and the Rank of the transformation. If you do notneed a vector, then place zeros for all entries of that vector (for example, if you only need 2 vectors for the basis, then fill in the firsttwo vectors and make all subsequent vectors have 0 for all boxes).a1) Let T b- B - Lla+1b+1c2a+3b+3c]-la + (-2)b+ (-2)c 3a+3b+3ci) A basis for Ker(T) would be:ii) The Nullity of T is:iii) The Rank of T is:2) Let T(a + bx + cx² + dx³) =i) A basis for Ker(T) would be:ii) The Nullity of T is:iii) The Rank of T is:3) Let Tab[ d f[def=1a2b+1c + 1d[la+16+2c+2d2a+36 + 4c+ 2d -la + (-3)6 + (-1)c+2d]la+(-1)b+1c+ (-1)d + 2e+4f2a+(-1)b+4c+4d + 6e + 12fOa+(-1)b+(-1)c+ (-4)d + (-1)e + (-2) f6a+(-3)b+11c + 10d + 18e + 34fi) A basis for Ker(T) would be:

For a linear transformation T, the kernel (Ker(T)) is the set of all vectors that are mapped to the…

Answered: For each linear transformation below,…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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For each transformation below, determine a basis for (Ker(T))↓. Note that if you do not need a basis vector, then write 0 for all entries of that basis vector. For example, if you only need 2 vectors in your basis, then write 0 in all boxes corresponding to the third vector 1) Let T c = 1a + 2b + 1c+3d + (−11) e+ (−la + (−1) b + (−2) c + Od + 7e) x. El Then a basis for (Ker(T)) would be:

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